University of Texas at AustinGIS in Water ResourcesProfessor: Dr. David Maidment

Probabilistic Model for Flooding in Guadalupe RiverBy Andres Perez

Objectives Find the monitoring point from ARC GIS Obtain hydrologic data from USGS Use the probabilistic models Obtain values of the parameters in the probabilistic models Use the Chi-square statistics test Obtain maximum flow values for 25, 50, and 100 years

Guadalupe River basin

2 Parameter Log Normal Distribution

The probability density function for the Log Normal Distribution is:

where:x = hydrologic data y = ln(x) natural log of xmy = mean of the population ysy = variance of the population of yDistribution Model for Maximum Flow in Rivers

The distribution model for predict the maximum flows for different period return are:1. 2 Parameters log normal2. 3 Parameters log normal 3. Extreme type I4. Pearson III5. Log Pearson III6. Gamma 3 parameters

a. Maximum Likelihood Estimation

The maximum likelihood estimates the distribution parameters such that product of the likelihoods of the individual events (L) is maximized. In terms of an equation this becomes an estimation of a, b ... such that

is maximized.b. Method of Moments EstimationThe method of moments uses the calculation of the rth moment about the origin of a distribution.

The probability function p(x) is then directly substituted into the equation and the distribution parameters are solved for directly. Estimation of the Parameters of Distribution Model

HYDROLOGIC DATA

From USGSProcess of down from web:www.USGS.gov/Maps, Products & Publications/National water-Data-NWISweb/Surface Water/Texas/Peak-flow data/Station Cuero ID: 08175800)

De Witt County, TexasHydrologicUnitCode 12100204Latitude 2905'25", Longitude 9719'46" NAD27Drainagearea 4,934 squaremilesContributingdrainagearea 4,934 squaremilesGagedatum 128.64feetabovesealevel NGVD29

RESULTSGraphics of Distribution ModelSoftware: SMADA http://cee.ucf.edu/software/

CHI SQUARE TESTFor doing the Chi-square test the equation is Wherek, is the data are divided interval of class

Oi, is the observed frequency for interval

Ei, is the expected frequency for interval

This test is for choose the better model probabilistic that better adjust or represent to the data from the river.Result of Chi square test of Log Normal 2 parameters

Conclusion of Chi square test:Chi square calculated is compare with the value Chi square from table

Then9.133 < 14.07 is good6.315 < 14.07 is good this is better Log Pearson III

Result of Chi square test of Log Pearson type IIIWhereK-1-p is degrees freedomp is quantity of parameter to estimatea is significance level

k Interval12345678910Low limit04704.99409.714141.518819.323524.128228.932933.737638.542343.2Upper limit4704.814141.414114.418819.22352428228.832933.637638.442343.24700000Oi38584101210Ei3875332119(Oi-Ei)2/Ei000.5711.80.3330.52010.1116.315

The better probabilistic model after Chi square test Cuero Station is : Log Pearson Type III

RESULT

Summary of Maximum Flow in Guadalupe River for different of Return of Period ( CFS)

NName station Return Period ( Years) Better Model2550100200Probabilistic1Victoria137947.90196129.90269144.90359549.002 Parameter Log Normal2Cuero181606.80295073.80467236.30725641.00Log Pearson 3New Braunfels69183.98105698.80155166.30220984.50Log Pearson 4Sattler25583.6035240.0146579.7959798.853Parameter Log Normal5Comfort131107.60189152.00260230.60345443.00Log Pearson6Kerrville141994.00187003.00234840.10285210.30 Pearson 7Hunt67744.1985524.45103929.50122910.30 Pearson

Return of Period of25 Years

Return of Period of50 Years

Return of Period of100 Years

Picture flooding Guadalupe River in Victoria October 20 1998Deaths and Damages During the 1998 Flood

http://pubs.usgs.gov/fs/FS-147-99/

ConclusionIn 1932, the historic discharge maximum peak was in the high basin, and in 1998 it was in the low basinThe value of these two years (1932 and 1998) largely distorted the probabilistic models. The probabilistic models, which are better adjusted to the peak stream flow, are Pearson Type III and Log Normal.The maximum value of flow shows the spatial variability of the storm in the basin.

Thank You